I'm editing a math word problem that has the following ambiguous set up.

A florist has 18 carnations, 24 daisies, and 12 lilies. She wants to
make flower arrangements that each have the same number of each type
of flower.

The question is about greatest common factors, so the intended interpretation is that each arrangement has c carnations, d daisies, and l lilies. However, the second sentence can also be interpreted as meaning each arrangement has n carnations, n daisies, and n lilies.

How can I reword the second sentence to ensure the first interpretation without resorting to technical descriptions like above? (Added difficulty: the question is for 6th graders.)

Edit:
I should add that test items are best when they are clear and concise. I'm looking for a solution that is both.

10 Answers
10

Rather than ending the sentence with “that each have the same number of each type of flower”, end it with “that each have the same number of lilies, the same number of daisies, and the same number of carnations”.

A florist has 18 carnations, 24 daisies, and 12 lilies. She [wants to sell all her flowers, and she] knows that everyone will want exactly the same bunch as everyone else: no one will want more carnations or fewer lilies or daisies than the next person. What’s the greatest number of bunches can she make?

I’ve added the bit about wanting to sell all her flowers, because otherwise a correct answer would be 12 (if each bunch has one of each flower and she fails to sell 6 carnations and 12 daisies).

Use of “greatest” (thanks to Andrew Leach for pointing out the need for revision here) clues students studying greatest common divisors in to what the question is after.

Thanks. The final sentence of the question (not shown) specifies that she has no flowers left over, so that much is taken care of. I mostly wanted a way to get around this specific wording issue.
– ExcellllAug 16 '12 at 21:25

I like the wording, but there is still more than one correct answer: 3 bunches of 6/8/4 or 6 bunches of 3/4/2. That's probably a deficiency in the original premise, but should there be an extra sentence "She needs to make the largest bunches she can" or "She needs to make as many bunches as she can"? Or, indeed, is the right answer that there are two answers?
– Andrew Leach♦Aug 16 '12 at 21:30

@AndrewLeach. You’re right! There’s an implication, but no explicit statement, that the highest number of bunches is sought. I’ll fix it.
– Daniel HarbourAug 16 '12 at 21:41

A florist has 18 carnations, 24 daisies, and 12 lilies. She wants to
make flower arrangements in such a way that each arrangement has the
same number of carnations, daisies, and lilies as every other
arrangement.

Might it be better to change this to "...have the same combination of all three types of flowers." I could make the same arrangements using only one type of flower and discard the rest, otherwise.
– GaffiAug 16 '12 at 21:19

A florist has 18 carnations, 24 daisies, and 12 lilies. She wants to make arrangements using all her flowers where the number of carnations is the same in each, as are the number of daisies, and lilies.

A florist has 18 carnations, 24 daisies, and 12 lilies. She wants to make flower arrangements where there are the there are a certain number of carnations, daisies, and lilies in each arrangement. The number of each kind of flowers is the same in every arrangement, but not necessarily the same as the number of the other types.